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A General Equilibrium Model with Impersonal Networking Decisions and Bundling Sales Ke Li and Xiaokai Yang The first version: July, 2001
The paper develops a general equilibrium model of impersonal networking decisions and bundling sales. It departures from the other models of bundling and tying by allowing substitution between goods, flexible quantities of goods, resale of any goods, competitive market, and ex ante identical utility function for all individuals. Hence, interactions and feedback loops between quantities, prices, network effects of division of labor, transaction costs, self-interested decisions, income, and productivity can be investigated. Inframarginal analysis (total cost-benefit analysis across corner solutions in addition to marginal analysis of each corner solution) of the model shows that the function of bundling sales in a competitive market is to get intangible information goods involved in the division of labor and commercialised production, meanwhile avoiding direct pricing of such goods, thereby promoting division of labor and aggregate productivity. According to this theory of bundling, bundling in a competitive market is Pareto efficient and it plays a very important role to utilize positive network effects of division of labor on aggregate productivity. Antitrust prosecution should pay more attention to the intention to block free entry rather than bundling itself. Acknowledgment: We are grateful to Paul Milgrom, Monchi
Lio, Yew-Kwang Ng, and participants of International Symposium of
Economics of e-Commerce and Networking Decisions, held on 6-7 July
2001 at Monash University, for helpful comments. We are solely responsible
for the remaining errors. The purpose of the paper is to investigate the function
of a particular type of bundling sales in exploiting network effects
of the division of labor and in promoting productivity progress. We
motivate this task from the following perspectives. First we compare
it with the existing literature of bundling and tying sales. We then
consider some common internet phenomena which cannot be predicted
by the existing literature. Finally, we motivate the research of effects
of bundling sales on the network size of division of labor by comparing
our task with the literature of endogenous specialization and network
effects of division of labor. An extensive literature has been developed to investigate
the role of bundling and tying sales (Bursten, 1960, Stigler, 1963,
Adams and Yellen, 1976, Schmalensee, 1984, McAfee, McMillan, and Whinston,
1989, Whinston, 1990, Hanson and Martin, 1990, Varian, 1995, 1997,
and Bakos and Brynjolfsson, 1999a, b). This literature focuses on
bundling and tying that is associated with monopoly power. The following
assumptions are made in this literature. Each consumer consumes at
most one unit of a good and has constant valuation of the one unit
of good. Resale of a good is not allowed. In addition, differentiated
prices cannot be directly charged for individuals with differentiated
valuations of goods because of un-observability of such valuations.
The assumptions imply that utility is not specified as a function
of amounts of all consumption goods and that no substitution between
goods is allowed (so-called independent valuations). Hence, interesting
interactions and feedback loops between consumption quantities, prices,
income, production decisions, and substitution between goods, which
are the focus of a standard general equilibrium analysis, are not
investigated in this literature. With the quite specific assumptions,
it is easy to see that bundling can impose indirect price discrimination
under a uniform price of a bundle of goods. Bakos and Brynjolfsson
(1999a, b) have nicely presented the intuition about this function
of bundling. In this literature, research results on welfare effects
of bundling are inconclusive. Adams and Yellen (1976) emphasize that
adverse effects of bundling on welfare come from monopoly power rather
than bundling itself. Bowman (1957), Blair and Kaserman (1978), Grimes
(1994), Delong (1998), Chae (1992), Fishburn, Odlyzko and Siders (1997),
Varian (1995), Chuang and Sirbu (1999), and Bakos and Brynjolfsson
(1997, 1999) pay more attention to positive welfare effects of bundling.
Matutes and Regibeau (1992), Tirole (1989, pp. 146-48), and Martin
(1999) pay more attention to adverse welfare effects of tie-in sales.
Whinston (1990) shows that welfare effects of tying in an oligopoly
regime are ambiguous. Bakos and Brynjolfsson, (1999b, p. 3) defend their
position by arguing that bundling sales with zero prices of some services
is a phenomenon of disequilibrium. We disagree. Zero price of a good
implicitly bundled with goods of positive prices can be a general
equilibrium phenomenon. A conventional market for petrol and air pump
services may illustrate our point. There are many petrol stations
which sell petrol at a competitive price and provide air pump services
free of charge. This market structure has been in place for long time.
The bundling of petrol and air pump services must be a general equilibrium
phenomenon. In this market, all consumers' preferences for petrol
and air pump service might be very similar, so that the rationale
for the type of bundling in the existing literature is irrelevant.
The intuition for this phenomenon is quite straightforward. Pricing
of air pump services and collection of related payment involves transaction
cost to consumers as well as to petrol stations (waiting time, inconvenience,
and tangible resource cost for pricing and payment collection). If
the production cost of such services can be added to the price of
petrol which is complementary to air pump services, then such transaction
cost can be avoided. Bundling sales may incur endogenous transaction
costs which are the distortions caused by individuals who use air
pump services but do not buy petrol from the same petrol station.
But as long as reduction of exogenous transaction costs of pricing
process of air pump services outweighs the increase in endogenous
transaction cost, a competitive market will generate pressure to compel
all petrol stations to implement such a bundling price structure.
We call this phenomenon implicit bundling which charges a positive
price of a good and zero price of another good without an explicit
bundle. Implicit bundling is closer to mixed bundling than pure bundling
investigated in the existing literature. Other implicit bundling cases
include TV programs (TV shows are free of charge and associated advertisements
are paid at positive prices by companies selling goods to viewers
of TV programs) and an automobile company's marketing operation with
positive prices of cars and free internet purchase services. Here,
the key point is that competition pressure and prohibitively high
pricing cost of some goods are essential for zero prices of goods
bundled with goods of positive prices. Therefore, we need a model
without monopoly power and with transaction costs and competitive
(implicit) bundling. This paper will formalize this story using a
general equilibrium model with well specified ex ante identical utility
and production functions for all individuals. We shall tell the story by formulating the trade-off
between positive network effects of division of labor on aggregate
productivity and transaction costs. As suggested by Allyn Young (1928),
network effect is a notion of general equilibrium. Not only the network
size of division of labor depends on the extent of the market (the
number of participants in the network of division of labor), but also
the number of participants is determined by all individuals' participation
decisions in the network of division of labor, which relate to their
decisions of their levels of specialization. This circular causation,
noted by Young, is of course an essential feature of general equilibrium,
analogous to the circular causation between quantities and prices
in the fixed point theorem (each individual's quantities demanded
and supplied depend on prices, while the equilibrium prices are determined
by all individuals' decisions of quantities). Hence, a partial equilibrium
model, such as those in the existing literature of bundling, does
not work for our task. Moreover, since we need an assumption of competitive
market for investigating network effects of division of labor, we
are not confined to the strategic networking decision which is associated
with monopoly power. We need a general equilibrium model of impersonal
networking decisions to investigate infinite feedback loops between
network size of division of labor, each person's participation decision,
prices, quantities, and different markets. Yang (2001) and Sun, Yang,
and Yao (1999) have drawn the distinction between the strategic networking
decision and the impersonal networking decision. For the latter, each
decision maker is not concerned with whom she has a trade connection
to. She is concerned with how many goods she will trade and how many
she will self-provide. Her decision in choosing the number of types
of traded partners determines her trade network size and pattern.
Impersonal networking decisions take place in a market where no body
can manipulate prices, so that implicit bundling with zero prices
of some goods may emerge from competitive pressure and free entry.
Such impersonal networking decisions generate network effects of division
of labor that are not network externalities since we assume that each
individual is capable of conducting inframarginal analysis (total
cost-benefit analysis across corner solutions in addition to marginal
analysis of each corner solution). Inframarginal analysis means that
each individual is capable of not only choosing locally optimum resource
allocation for a given trade network pattern using standard marginal
analysis, but also choosing a globally optimal trade network pattern
by comparing several locally optimum values of objective functions.
Formally, inframarginal analysis is non-linear programming. Coase
(1946, 1960), Buchanan and Stubblebine (1962), and Yang (2001) have
shown that a lot of so-called network externalities can be internalized
by individuals' inframarginal decisions. They are considered externalities
by many economists since these economists assume, naively, that individuals
are incapable of doing inframarginal analysis. Many contributors to
the literature of inframarginal analysis of network effects of division
of labor and impersonal networking decision (see surveys of this literature
by Yang and Ng, 1998 and by Yang, 2001, and references there) have
shown that marginal cost pricing does not work when individuals conduct
inframarginal analysis. Hence, non-marginal cost pricing is compatible
with a competitive market with localized increasing returns and impersonal
networking decisions. In this paper, we will specify a general equilibrium
model with a continuum of ex ante identical consumer-producers who
prefer diverse consumption and specialized production due to economies
of specialization in production of three goods. There is the trade-off
between transaction costs and positive network effects of division
of labor on aggregate productivity. Hence, if the transaction cost
coefficient for a unit of goods traded is very large, the positive
network effect is outweighed by transaction costs. Therefore, individuals
choose autarky where market, institution of the firm, and bundling
sales do not occur. As the transaction cost coefficient decreases,
the general equilibrium discontinuously jumps to a higher level of
division of labor. Markets emerge from the division of labor. However,
if the transaction cost coefficient for labor is smaller than that
for goods, the institution of the firm and related labor market emerge
from the division of labor. Otherwise, the markets for various goods
will be used to organize the division of labor in the absence of the
institution of the firm and related labor market. If the transaction
cost coefficient for a good is extremely large and the equilibrium
level of division of labor is sufficiently high, then this good will
be implicitly bundled with other goods to avoid prohibitively high
pricing cost, meanwhile getting this good involved in the large network
of division of labor and commercialised production. Intuitively, this story can be told as follows. Suppose
that an automobile manufacturer, such as General Motor, sells automobiles
and internet services for purchasing cars online. Automobiles are
tangible goods which are easy to price, but internet services are
intangible, very difficult to price. General Motor can bundle two
goods together by providing free internet services and by adding the
operation cost of internet services to the price of automobiles. If
such bundling can save consumers' transaction costs incurred in a
purchase deal in excess of the added cost to the price of automobiles,
General Motor will have a competitive edge compared to other automobile
manufacturers who do not provide such bundled deal. Then a competitive
pressure in the market will force all manufacturers to provide such
bundled deal. Here, monopoly power, constant and independent valuations
of one unit of good, non-resale, and other peculiar assumptions are
not needed. In addition, even if all individuals have ex ante identical
utility function which allows substitution between goods, productivity
gains from bundling may be generated by network effects of division
of labor. Without bundling, involvement of the good with prohibitively
high transaction cost coefficient in a high level of division of labor
and avoidance of direct pricing cost of such a good cannot coexist.
Hence, positive network effects of division of labor on aggregate
productivity cannot be fully exploited. With the bundling, both of
the tasks can be achieved at the same time. Therefore, the network
effects can be fully exploited and aggregate productivity can be promoted
by the bundling. It is interesting to see that bundling in a competitive
market has very important productivity implications even if all individuals
have ex ante identical utility and production functions and substitution
between different goods is non-trivial. This paper proceeds as follows. Section 2 is devoted to describe the model. Section 3 solves equilibrium and its comparative statics and reports main findings. The final section concludes the paper. Inframarginal Economics Society www.inframarginal.com |